#bohr model

So Heisenberg says that the more precisely/accurately we know the momentum of a particle, the less precisely/accurately we know the particle's position, and vice versa. This is because of particle-wave duality, so it's just the nature of things, it's not because of the accuracy limits of our measuring instruments. We know that light isn't just a wave because if light were just a wave, the photoelectric effect wouldn't happen. If light were just a wave, we don't have threshold frequencies because we'd just need to shine a light of any frequency on an electron long enough to excite it and eject it.

Heisenberg reasoned that light acts particle-like because light is a wave packet. In a wave packet, there are many waves of different de Broglie wavelengths. Sometimes they're in phase and sometimes they're out of phase. When they're in phase, you get constructive interference that forms a photon and when they're out of phase, you get destructive interference that cancels out the waves (observed as "there is space between the wave packets"). So what you get is a beam of photons like this:

In other words, it's impossible to have a single frequency of light. If light behaves like particles, the only way that's possible is if no matter how good we are at isolating frequencies of light, what we end up with is a wave packet - a spread of frequency, an uncertainty in frequency.

Bohr and Rydberg were thinking of the electron in hydrogen like it emits or absorbs a single frequency of light as it moves between distinct energy levels, like the electron has a definite energy. But Heisenberg says that the photon must have a spread of frequencies to exist as a photon, and if there's a spread of frequencies of EMR emitted or absorbed by the electron, then the electron also must have a spread of energies, an uncertainty in energy in the atom because frequency is directly proportional to energy. This means that the energy in E = hv can't be known exactly.

Heisenberg's uncertainty is a consequence of the fact that to measure/observe stuff at the atomic level, we must disturb it (e.g. bounce light off of it to see it) and that disturbance is always significant at the atomic level. In contrast, such a disturbance would be insignificant for the most part for things at the macroscopic level. Thus, Bohr's model can't be correct because it says that electron momentum and therefore energy is always well defined. So we need a new model.

Mathematically, Heisenberg's uncertainty principle looks like this in one dimension (x), where h/4*pi is the lowest amount of uncertainty you can get:

Basic derivation:

Introduction to the Bohr Model

Introduction to the Bohr Model Bohr model of the atom was proposed by Neil Bohr in 1915. It came into existence with the modification of Rutherford’s model of an atom. Rutherford’s model introduced the nuclear model of an atom, in which he explained that a nucleus (positively charged) is surrounded by negatively charged electrons. Bohr modified this atomic structure model by explaining that…